Ergodic properties and thermodynamic behavior of elementary reversible cellular automata. I. Basic properties

This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of fully-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems.     

A series of dinuclear homo- and heterometallic complexes with two or three bridging sulfido ligands derived from the tungsten tris(sulfido) complex [Et(4)N][(Me(2)Tp)WS(3)] (Me(2)Tp = hydridotris(3,5-dimethylpyrazol-1-yl)borate)

The generation of heterobimetallic complexes with two or three bridging sulfido ligands from mononuclear tris(sulfido) complex of tungsten [Et(4)N][(Me(2)Tp)WS(3)] (1; Me(2)Tp = hydridotris(3,5-dimethylpyrazol-1-yl)borate) and organometallic precursors is reported. Treatment of 1 with stoichiometric amounts of metal complexes such as [M(PPh(3))(4)] (M = Pt, Pd), [(PtMe(3))(4)(micro(3)-I)(4)], [M(cod)(PPh(3))(2)][PF(6)] (M = Ir, Rh; cod = 1,5-cyclooctadiene), [Rh(cod)(dppe)][PF(6)] (dppe = Ph(2)PCH(2)CH(2)PPh(2)), [CpIr(MeCN)(3)][PF(6)](2) (Cp = eta(5)-C(5)Me(5)), [CpRu(MeCN)(3)][PF(6)], and [M(CO)(3)(MeCN)(3)] (M = Mo, W) in MeCN or MeCN-THF at room temperature afforded either the doubly bridged complexes [Et(4)N][(Me(2)Tp)W(=S)(micro-S)(2)M(PPh(3))] (M = Pt (3), Pd (4)), [(Me(2)Tp)W(=S)(micro-S)(2)M(cod)] (M = Ir, Rh (7)), [(Me(2)Tp)W(=S)(micro-S)(2)Rh(dppe)], [(Me(2)Tp)W(=S)(micro-S)(2)RuCp] (10), and [Et(4)N][(Me(2)Tp)W(=S)(micro-S)(2)W(CO)(3)] (12) or the triply bridged complexes including [(Me(2)Tp)W(micro-S)(3)PtMe(3)] (5), [(Me(2)Tp)W(micro-S)(3)IrCp][PF(6)] (9), and [Et(4)N][(Me(2)Tp)W(micro-S)(3)Mo(CO)(3)] (11), depending on the nature of the incorporated metal fragment. The X-ray analyses have been undertaken to clarify the detailed structures of 3-5, 7, and 9-12.     

Time Courses and Time‐Resolved Spectra of Firefly Bioluminescence Initiated by Two Methods of ATP Injection and Photolysis of Caged ATP

The time‐dependent characteristics of firefly bioluminescence initiated by manual injection of adenosine triphosphate (ATP) into buffer solution containing luciferin (Ln), luciferase (Luc) and Mg²⁺ were measured with a resolution of 10 ms, and compared with those obtained by photolysis of caged ATP. The time course depends on pH; both rise and decay rates decrease when pH is lowered from 7.8 to 6.8. In contrast, the parameter λ in the kinetic formula related to diffusion of ATP is almost independent of pH. The pH dependence of the time course of bioluminescence can be explained by the same pH tendency as the rate of ATP binding at the active site of Luc. The time‐resolved spectra can be decomposed into two Gaussian components with maxima at 2.2 and 2.0 eV. At pH 7.8, the band at 2.2 eV is more intense than that at 2.0 eV for all three concentration conditions. At lower pH, the band at 2.2 eV becomes weaker than that at 2.0 eV. The intensity ratio of the 2.0 and 2.2 eV bands is constant for duration time of 600 s for both injection and photolysis experiments, and the above conclusions are unaffected by the concentration ratio [Ln]/[Luc].     

The reaction process of firefly bioluminescence triggered by photolysis of caged-ATP

The reaction process of firefly bioluminescence was studied by photolyzing caged-ATP to adenosine triphosphate (ATP) within 100 ms. The intensity of luminescence increases markedly to reach a maximum within 1 s, maintains almost the same intensity up to 5 s and then decays monotonically. The rise γ(1) and decay γ(2) rate constants were determined to be about 5 s(-1) and 1 × 10(-2) s(-1), respectively, so as to phenomenologically fit the time course. A second luminescence peak appears after around 350 s. The dependence of the rate constants on the concentrations of reactants and a viscous reagent revealed that two kinds of reaction contribute the observed time course: (1) an intrinsic reaction by ATP photolyzed from caged-ATP that is already trapped in luciferase; and (2) a diffusion-controlled reaction by free ATP in the buffer solution outside luciferase. Numerical analysis based on reaction kinetics related γ(1) and γ(2) to the rate constants of a three-step reaction model, and accurately described the effects of concentration of reactants and a viscous reagent on the time courses of bioluminescence. Thus, it has been clearly concluded that the binding mode of caged-ATP at the catalytic center of luciferase is very different from that of ATP.     

Dihydrogen activation by sulfido-bridged dinuclear Ru/Ge complexes: insight into the [NiFe] hydrogenase unready state

A S/SH bridged hetero-dinuclear Ru/Ge complex cation reacted with H(2) to afford the μ-S/μ-H complex. The reaction was considerably slower compared to that of the μ-S/μ-OH complex. Thus, the μ-S/μ-SH and μ-S/μ-OH complexes might provide models for the unready and ready states, respectively, of [NiFe] hydrogenase.     

Spatial theory for algebras of unbounded operators

In this paper, the spatial theory of ¹-automorphisms is investigated in the context of algebras of unbounded operators. In particular, it is shown that ¹-automorphisms, satisfying some order relation, of the Op¹-algebra generated by the position and momentum operators q_j, p_j(j=1,...., n) on the Schwartz space $\text{I}\text{(}\text{R}{}^{\mathrm{n}}\text{)}$ are unitarily implemented.     

Superconductivity in entirely end-bonded multiwalled carbon nanotubes

We report that entirely end-bonded multiwalled carbon nanotubes (MWNTs) can exhibit superconductivity with a transition temperature (T(c)) as high as 12 K, which is approximately 30 times greater than T(c) reported for ropes of single-walled nanotubes. We find that the emergence of this superconductivity is highly sensitive to the junction structures of the Au electrode/MWNTs. This reveals that only MWNTs with optimal numbers of electrically activated shells, which are realized by end bonding, can allow superconductivity due to intershell effects.     

Local structural analysis of In-doped Bi2Se3 topological insulator using X-ray fluorescence holography

We performed X-ray fluorescence holography measurements on an In-doped Bi₂Se₃ topological insulator and obtained an in-plane atomic image in the vicinity of In. We found that atomic images at the positions of the first nearest neighbors (NNs) are very weak whereas those at the positions of the second and the third NNs are relatively strong. On the basis of the fact that In is half of the atomic number of Bi, we attributed the origin of this feature to the clustering of the In atoms in the Bi plane. We calculated the intensity of the atomic images and confirmed that the formation of In cluster results in a decrease by 30% in the first NN atomic image intensity. However, the decrease in the magnitude is not enough to explain the experimental results, suggesting another contribution such as the lattice distortions. The effect of the lattice distortion on the atomic image intensity is discussed on the basis of the simulation including the positional fluctuation of In atoms.